Regions

A region is the open set on one side of a closed curve or closed path.

Simply connected

A simply connected region is one bounded by a single closed curve or path; topologically, it has no holes. The Interior1CRegion and Exterior1CRegion types represent the interior and exterior of such a boundary, respectively. The preferred method for constructing a value of one of these types is to use interior or exterior with a closed curve or path as argument. If the given curve is bounded, these constructors ignore its orientation and select the bounded or unbounded region it defines, respectively. For an unbounded boundary curve, points “to the left” of it are considered the interior.

There are also methods to facilitate construction of important common regions. For disks there are

• disk(C) for a Circle C
• disk(center, radius)
• unitdisk

For half-planes there are

• halfplane(L) for a Line L
• upperhalfplane, lowerhalfplane, lefthalfplane, righthalfplane

Multiply connected

The ExteriorRegion class represents a region that is exterior to several closed curves or paths, which are given as an array of such objects.

The InteriorRegion class represents a region that is interior to one outer closed curve or path and exterior to several inner closed curves or paths, which are given as an array of such objects. The particular case of a doubly connected region can be constructed by between(outer, inner), giving the two boundary components. The given orientation is ignored for any bounded component.

Annulus

An Annulus is the doubly connected region between two concentric circles. Construction is by Annulus(outer, inner), where Circle values are given explicitly, or by Annulus(outrad, inrad, center=0), giving the radii and optionally the center.

Methods

Here R is a Region subtype and z is a number.

Method	Description
R.boundary()	Boundary curve(s)/path(s) of a region.
R.contains(z)	Determine whether z is in R.
R.isfinite()	Determine whether the region is bounded.

Default implementations are provided for +, -, *, /, performing translation, rotation, and scaling.

Method	Description
R.outerboundary()	Curve/path of the outermost boundary, if it exists.
R.innerboundary()	Curve(s)/path(s) of inner boundaries (that R is exterior to).

Examples

from cxregions import *
import numpy as np
import matplotlib.pyplot as plt

Detected IPython. Loading juliacall extension. See https://juliapy.github.io/PythonCall.jl/stable/compat/#IPython

Here is a “dog bone” region.

a = Arc(-1, 1, -1j)
right = Path([4 + 1j + a, 4 - 1j - 1j * a])
s = Segment(-3 + 1j, 3 + 1j)
p = ClosedPath([s, *right, -s, *(-right)])
r = interior(np.exp(1j * np.pi / 4) * p)
print(r.boundary.arclength())

30.84955592153876

A multiply-connected exterior region:

c = Circle(0, 1) t = n_gon(3) s = n_gon(4) exterior_region = ExteriorRegion([c, 3 + s, 6 + t]) print(exterior_region)